What is the difference between slander and harment?

My neighbors are going out of they're way to tell all of my neighbors how horrible me and my boyfriend are and that they should watch out for us. All we have done is try to keep to ourselves, keep their pot smoke out of our apartment and try to get them to keep their music down so that our floor isn't vibrating. He's now at the point that he's doing it in front of us. What can we do? Do we have legal grounds? We also have a witness who heard him doing this?